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The function f(x)=2[sgn(2x)]+2 has...

The function `f(x)=2[sgn(2x)]+2` has

A

removable discontinuity

B

irremovable discontinuity

C

no discontinuity at x = 0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=2[ sgn(2x)] +2={(0",",x lt 0),(2",",x =0),(4",", x gt 0):}`
So, clearly f has irremovable discontinuity at x = 0.
`[ because lim _(x to 0^(+)) f(x) ne lim_(x to 0^(-)) f(x)]`
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